Recent literature emphasises the role of exploration, designerly play, creative thinking, and handling of materials in the beginning years of learning. This paper reports findings from a study involving 24 children (aged 4 to 10 years), where the researchers engaged with four-story contexts (tasks) that had embedded problem scenarios. In response to problems presented in the stories, children were invited to express their design ideas through drawings and oral expressions. Analysis of the children's work yielded insights into design thinking and revealed the cognitive strategies children used for addressing different kinds of problem scenarios. The experience offers significant takeaways for designing contextually appropriate curricular engagements in the early and primary years.